diff --git a/crates/sylpheed-formats/examples/main_menu_element_extents.rs b/crates/sylpheed-formats/examples/main_menu_element_extents.rs
new file mode 100644
index 00000000..c0521681
--- /dev/null
+++ b/crates/sylpheed-formats/examples/main_menu_element_extents.rs
@@ -0,0 +1,46 @@
+//! What elements sit under the port's hot residual tiles on the main menu?
+//!
+//! `sylpheed-port` mapped the menu's edge residual at 64 px tiles and handed over
+//! coordinates without names — the element inventory is this side's. Hot tiles
+//! cluster at x 384–704, y 64–256, hottest at (512,128).
+//!
+//! ⚠️ Their tiles are in the frame they compare in; this prints DESIGN space, and
+//! the two differ by the capture offset (capture_y ≈ 64.8 + 0.992·design_y). Both
+//! readings are printed so the mapping is not assumed.
+//!
+//!     cargo run -p sylpheed-formats --example main_menu_element_extents
+use sylpheed_formats::{pak::PakArchive, ui_layout};
+use std::path::PathBuf;
+
+fn main() {
+    let root = PathBuf::from(std::env::var("SYLPHEED_DISC").expect("SYLPHEED_DISC"));
+    let ar = PakArchive::open(root.join("dat/GP_TITLE.pak")).expect("GP_TITLE");
+    let by = ar.read(&ar.entries()[5]).expect("entry 5");
+    let b = ui_layout::parse_build(&by).expect("build");
+    println!("{:<26} {:>6} {:>6} {:>7} {:>7}  {}", "element", "x", "y", "pivot_x", "pivot_y", "sprite");
+    let mut rows: Vec<(i32, i32, String, String)> = b
+        .elements
+        .iter()
+        .map(|e| {
+            let k = e.rest();
+            (k.map(|k| k.x).unwrap_or(0), k.map(|k| k.y).unwrap_or(0),
+             e.name.clone(), e.sprite.clone().unwrap_or_default())
+        })
+        .collect();
+    rows.sort_by_key(|r| (r.1, r.0));
+    for (x, y, n, s) in &rows {
+        // flag anything whose rest position lands in the hot band, read both ways
+        let cap_y = 64.82 + 0.9919 * (*y as f64);
+        let hot_design = (384..=704).contains(x) && (64..=256).contains(y);
+        let hot_capture = (384..=704).contains(x) && (64.0..=256.0).contains(&cap_y);
+        let mark = match (hot_design, hot_capture) {
+            (true, true) => " <- HOT both readings",
+            (true, false) => " <- hot in DESIGN space",
+            (false, true) => " <- hot in CAPTURE space",
+            _ => "",
+        };
+        println!("{n:<26} {x:>6} {y:>6} {:>7} {:>7}  {s}{mark}",
+                 b.elements.iter().find(|e| &e.name == n).map(|e| e.pivot_x).unwrap_or(0),
+                 b.elements.iter().find(|e| &e.name == n).map(|e| e.pivot_y).unwrap_or(0));
+    }
+}
diff --git a/docs/re/data/menu-hot-tile-inventory.txt b/docs/re/data/menu-hot-tile-inventory.txt
new file mode 100644
index 00000000..77576901
--- /dev/null
+++ b/docs/re/data/menu-hot-tile-inventory.txt
@@ -0,0 +1,38 @@
+# What sits under the port's hot residual tiles on the main menu? 2026-08-31.
+#
+# sylpheed-port mapped the menu's edge residual at 64 px tiles and handed over
+# COORDINATES WITHOUT NAMES -- the element inventory is this side's. Their result:
+# hot tiles cluster at x 384..704, y 64..256, hottest (512,128) at 3.66x the median
+# tile, and NO tile in the hot region has moved (every |dx|,|dy| < 0.1 px against a
+# control reading a true 1 px at +0.949).
+#
+# ⚠️ COORDINATE FRAME. Their tiles are in the frame they compare in; the disc is
+# design space, and the two differ by the capture offset
+# (capture_y = 64.82 + 0.9919 * design_y). So both readings were tested rather than
+# one assumed -- and the answer does not depend on it: three elements are hot under
+# BOTH.
+#
+# ✅ ELEMENTS WHOSE REST POSITION FALLS IN THE HOT BAND (GP_TITLE entry 5):
+#
+#   ptframe1.t32   (440, 108)  pivot (124,140)   HOT under both readings
+#   ptbtn01.rat    (542, 162)  pivot ( 42, 22)   HOT under both -- the NEW GAME button
+#   pteff12.t32    (467, 180)  pivot (174,180)   HOT under both -- an effect element
+#   ptbtn02.rat    (542, 242)  pivot ( 58, 22)   hot in DESIGN space only
+#
+# 📌 THE HOT REGION IS NOT ONE ELEMENT. It is where a FRAME, a BUTTON and an
+# EFFECT overlap -- three elements of different kinds stacked in the same band.
+# That is consistent with their null result: they went looking for two families of
+# tile (edge-only versus hot-everywhere) and found one continuous population, so
+# the region has no character of its own.
+#
+# ⚠️ WHAT THIS DOES NOT SAY. It names what is THERE, not what is wrong. Their map
+# already excludes local displacement in these tiles, so this is not a misplaced
+# element; the inventory is offered as the next reader's starting point, not as a
+# diagnosis. The residual's cause remains open.
+#
+# 📌 AND A CONTROL LIMIT OF THEIRS THAT CHANGES HOW ANY SLOPE READS: a known +2 px
+# displacement localises perfectly but reads back +0.839, because the slope is a
+# linearisation (residual ~ dx * gradient) that saturates once dx approaches the
+# width of an edge. So their +1 px control gives localisation AND magnitude, the
+# +2 px control gives localisation and SIGN only, and **any slope they report is a
+# FLOOR on the displacement, never a ceiling**.